Bonded Interactions and the Crystal Chemistry of Minerals: a Review # Z

This article is protected by German copyright law. You may copy and distribute this article for this article and distribute copy You may law. copyright German by protected is This article Z. Kristallogr. 223 (2008) 1–40 / DOI 10.1524/zkri.2008.0002 1 # by Oldenbourg Wissenschaftsverlag, Mu¨nchen Bonded interactions and the crystal chemistry of minerals: a review G. V. Gibbs*,I, Robert T. DownsII, David F. CoxIII, Nancy L. RossI, Charles T. PrewittII, Kevin M. RossoIV, Thomas LippmannV and Armin KirfelVI I Department of Geosciences, Virginia Tech, Blacksburg, VA 24061, USA II Department of Geosciences, University of Arizona, Tucson, AZ, 85721, USA III Department of Chemical Engineering, Virginia Tech, Blacksburg, Va. 24061, USA IV Chemical Science Division, and W.R. Wiley Molecular Sciences Laboratory, Pacific Northwest Laboratory, Richland, Washington, USA V GKSS, Max-Planck-Strasse, 21502, Geesthacht, Germany VI Mineralogisch Petrologisches Institut, Universitact Bonn, Poppelsdorfer Schloss, 53115, Bonn, Germany Received May 7, 2007; accepted August 15, 2007 Bond critical point / Silicates / Sulfides / character of the intermediate and shared bonded interac- Local energy densities / Eelectron density / Bond strength / tions. In contrast, the local kinetic energy density in- Electron lone pair domains / Molecular chemistry / creases with decreasing bond length for closed shell inter- Electrophilicity actions with G(rc) dominating V(rc) in the internuclear region, typical of an ionic bond. Abstract. Connections established during last century Notwithstanding its origin in Pauling’s electrostatic between bond length, radii, bond strength, bond valence bond strength rule, the Brown-Shannon bond valence for and crystal and molecular chemistry are briefly reviewed Si––O bonded interactions agrees with the value of the followed by a survey of the physical properties of the electron density, r(rc), on a one-to-one basis, indicating your personal use only. Other use is only allowed with written permission by the copyright holder. copyright by the permission with written allowed is only Other use only. use your personal electron density distributions for a variety of minerals and that the Pauling bond strength is a direct measure of r(rc), representative molecules, recently generated with first-prin- the greater the bond strength, the more shared the interac- ciples local energy density quantum mechanical methods. tion. Mappings of the Laplacian, the deformation electron The structures for several minerals, geometry-optimized at density distribution and the electron localization function zero pressure and at a variety of pressures were found to for several silicates are reviewed. The maps display hemi- agree with the experimental structures within a few per- spherical domains ascribed to bond pair electrons along cent. The experimental Si––O bond lengths and the the bond vectors and larger kidney-shaped domains as- Si––O––Si angle, the Si––O bond energy and the bond criti- cribed to lone pair electrons on the reflex sides of the cal point properties for crystal quartz are comparable with Si––O––Si angles. In the case of the nonbridging Si––O those calculated for the H6Si2O7 disilicic acid molecule, bonded interactions, the O atoms are capped by mush- an indication that the bonded interactions in silica are lar- room shaped domains. With few exceptions, the domains gely short ranged and local in nature. The topology of agree in number and location with those embodied in the model experimental electron density distributions for first VSEPR model for closed-shell molecules, defining reac- and second row metal M atoms bonded to O, determined tive sites of potential electrophilic attack and centers of with high resolution and high energy synchrotron single protonation. The electrophilicity of the O atoms compris- crystal X-ray diffraction data are compared with the topol- ing the Si––O––Si bonded interactions in coesite is indi- ogy of theoretical distributions calculated with first princi- cated to increase with decreasing angle, providing a basis ples methods. As the electron density is progressively for understanding the protonization of the structure. accumulated between pairs of bonded atoms, the distribu- The shapes and arrangements of the bond and lone pair tions show that the nuclei are progressively shielded as the features displayed by the bridging O atoms in quartz and bond lengths and the bonded radii of the atoms decrease. and the nonbridging O atoms in forsterite are transferable Concomitant with the decrease in the M––O bond lengths, on an one-to-one basis to sheet and chain magnesiosili- the local kinetic energy, G(rc), the local potential energy, cates that possess both bridging and nonbridging O atoms. V(rc), and the electronic energy density, H(rc) ¼ G(rc) þ The G(rc)/r(rc) ratio increases for each of the M––O V(rc), evaluated at the bond critical points, rc, each in- bonds along separate trends with decreasing bond length creases in magnitude with the local potential energy domi- and the coordination number of the M atom, suggesting nating the kinetic energy density in the internuclear region that the ratio is a measure of bond character. An examina- for intermediate and shared interactions. The shorter the tion of the interactions in terms of the jV(rc)j=G(rc) ratio bonds, the more negative the local electronic energy den- indicates that the Li––O, Na––O and Mg––O bonds are sity, the greater the stabilization and the greater the shared closed shell ionic interactions, that the C––O bond and one of the S––O bonds is shared covalent and that the Be––O, * Correspondence author (e-mail: [email protected]) Al––O, Si––O, B––O, P––O and S––O bonds are intermedi- This article is protected by German copyright law. You may copy and distribute this article for this article and distribute copy You may law. copyright German by protected is This article 2 G. V. Gibbs, R. T. Downs, D. F. Cox et al. ate in character. It is noteworthy that the classification clo- likewise be determined in a more accurate way and used sely parallels Pauling’s classification based on the electro- in the modeling and study of the individual bonded inter- negativity differences between the M and O atoms. actions. The electron density distribution is a property of Bond critical point properties calculated for Ni bearing “extraordinary” importance in that it contains in principle sulfides and high and low spin Fe bearing sulfides are dis- all of the information that can be known about a ground cussed. The properties correlate linearly, as observed for state material like a mineral or a representative molecule, the M––O bonds, with the experimental bond lengths, the including the kinetic, potential and total energies [3]. In- 2 shorter the bond lengths, the greater the r(rc) and r r(rc) deed, studies of bond lengths and electron density distribu- values. The high and low spin Fe––S data scatter along tions have played a key role in the development of a parallel but separate trends with the values of r(rc) and bonding theory and the crystal chemistry of minerals [4– 2 r r(rc) for a given low spin Fe––S bond length being 10]. Although these studies have done much to advance our larger than those calculated for a given comparable high knowledge and understanding of the bonded interactions, spin Fe––S bond length. The properties of the Ni––Ni our grasp of the crystal chemistry and the physical proper- bonded interactions calculated and observed for the Ni ties of minerals is still far from complete. In an important sulfides are virtually the same as those calculated for bulk step in the advancement of our understanding of crystal Ni metal. No bond paths were found between the Fe atoms chemistry, Bader and his colleagues [2] forged a powerful of the face sharing octahedra of troilite. The experimental and widely used theory during the last part of the 20th cen- bond critical point properties for the Ni sulfide heazlewoo- tury for classifying, characterizing and determining the dite, Ni3S2, are in close agreement with those calculated. bonded interactions for a wide variety of materials, includ- The jV(rc)j=G(rc) ratio indicates that the Fe––S, Ni––S and ing minerals in terms of the topological and physical proper- Ni––Ni bonded interactions are intermediate in character. ties of their electron density distributions, the local energy The successful reproduction of the bond lengths and an- density properties and the bond length variations. gles for several silicates, the comparable properties of the The topological and physical properties of the electron electron density distributions and the location of sites of density distributions determined since the latter part of last potential chemical reactivity recounted in the review bodes decade for a variety of minerals and representative mole- well for the exploitation of the properties of minerals and cules will be explored in this review in terms of (1) the the deciphering of crystal chemical problems, using first degree to which the properties of the experimental electron principles computational quantum chemical strategies. density distributions agree with those calculated with first principles quantum mechanical chemical methods, (2) the correspondence between the structural properties of a holder. copyright by the permission with written allowed is only Other use only. use your personal Introduction mineral and the physical properties of the electron density distribution, (3) the connection between the local

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